
We are using the description in [1]}.
For the above parameter array
the sequence \(\lbrace \theta _i\rbrace _{i=0}^d\)  (resp. \(\lbrace \theta ^*_i\rbrace _{i=0}^d\) ) is an ordering
of the eigenvalues of \(A\)  (resp. \(A^*\) ).
These orderings are standard [2]}.
We comment on the uniqueness of the parameter array.
Consider a parameter array (REF ) of \(A,A^*\) .
Then by [2]}
each of the following is a parameter array of \(A,A^*\) :
\(& ( \lbrace \theta _i\rbrace _{i=0}^d; \lbrace \theta ^*_i\rbrace _{i=0}^d; \lbrace \varphi _i\rbrace _{i=1}^d; \lbrace \phi _i\rbrace _{i=1}^d),&& ( \lbrace \theta _i\rbrace _{i=0}^d; \lbrace \theta ^*_{d-i}\rbrace _{i=0}^d; \lbrace \phi _{d-i+1}\rbrace _{i=1}^d; \lbrace \varphi _{d-i+1}\rbrace _{i=1}^d),\\& ( \lbrace \theta _{d-i}\rbrace _{i=0}^d; \lbrace \theta ^*_i\rbrace _{i=0}^d; \lbrace \phi _i\rbrace _{i=1}^d; \lbrace \varphi _i\rbrace _{i=1}^d),&& ( \lbrace \theta _{d-i}\rbrace _{i=0}^d; \lbrace \theta ^*_{d-i}\rbrace _{i=0}^d; \lbrace \varphi _{d-i+1}\rbrace _{i=1}^d; \lbrace \phi _{d-i+1}\rbrace _{i=1}^d).\) 
